2000/11/13 by Florin Rădulescu, Florin G. Radulescu, Radulescu, Florin G.
Mathematics · Physics and Astronomy · #46L54 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Mechanics and Applications #math.OA #msc:46L54
paper · pdf · doi:10.48550/arxiv.math/0011084
LaTeX2e amsart class; 17 pages (now single spaced); picture and minor corrections added
openalex publication_date 2000/11/13 · arxiv created 2000/11/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an inclusion of the form \Bbb C⊆ Mn(\Bbb C), where Mn(\Bbb C) is endowed with a state with diagonal weights λ=(λ1, ..., λn), we use Popa's construction, for non-tracial states, to obtain an irreducible inclusion of II1 factors, Nλ(Q)⊆ Mλ(Q) of index ∑ (1)/(λi). Mλ(Q) is identified with a subfactor inside the centralizer algebra of the canonical free product state on Q⋆ MN(\Bbb C). Its structure is described by ``infinite'' semicircular elements as in \citeRa3. The irreducible subfactor inclusions obtained by this method are similar to the first irreducible subfactor inclusions, of index in [4,∞) constructed in \cite Po1, starting with the Jones' subfactors inclusion Rs⊆ R, s>4. In the present paper, since the inclusion we start with has a simpler structure, it is easier to control the algebra structure of the subfactor inclusions.